Projectile Motion of a Golf Ball

Projectile Motion of a Golf Ball

by Sammy Stone

Video Analysis in Logger Pro

Golf Ball Projectile Video

Additional Video Information

Data Table

30 frames per second

height of wall: 1.5m

• The height of the wall in the background is 1.5 meters
• The total time the golf ball spent in the air (flight time) is approximately .7 seconds
• The golf club used to hit the ball was a 56 degree Wedge

(the future Catholic Tiger Woods )

Position versus Time Graph

X Position Versus Time Graph

The x and y components of a projectile are independent of each other...

Therefore:

• the x velocity is constant for it is unaffected by gravitational acceleration

This graph exemplifies this, as the horizontal or x velocity (the slope of the line) is a constant -5.268 m/s

The Physics of Golf

Calculations

Air Resistance is a very influential force on the trajectory a golf ball:

Y Position versus Time Graph

m/s

The Physics of Golf (Continued)

BECAUSE Friction between the ball and the air takes away some of the kinetic energy of the ball.

1. Initial Velocity: Vi^2 = Vx^2 +Vy^2

where Vx= -5.268 and Vy= 3.19m/s

Vi^2= 37.93 Vi=6.16

2. Angle of launch: tan = (Vy/Vx) = tan^-1 (3.19/-5.268)

=-31.2 degrees

If a golf ball didn't have any dimples and we neglect any other aerodynamic effects such as drag and wind, then the calculations would be as follows:

3. Range of Flight: X=Vix(t) time=.7, Vix=-5.268m/s

X=3.69m

• So dimples on a golf ball were added give the ball more lift and reduce drag during its flight which in turn increases the distance traveled

4. Maximum Height of the Golf Ball: y=(Visin )^2 /2g

y=(6.16sin-31.2)^2/19.6

y=.52 meters

Conclusion

When factoring in air resistance and drag, the trajectory of a golf ball is much shorter than when factoring without. This is a result of the great influence of these two forces on the tiny flying golf ball.

Sources:

• http://sportsnscience.utah.edu/the-in-depth-science-of-golf/

• http://www.golf-simulators.com/physics.htm

• The Magnus Effect:

As shown in this trajectory graph, the ball with dimples travels farther than the ball without

Calculations With Air Resistance

The following formulas can be used to make calculations of a golf ball while factoring in air resistance and drag:

Y Range:

Drag Force:

Where CD is the drag coefficient, A is the cross-sectional area of the ball, pρ is the air density, and v is the ball velocity

X Range:

Where c is 0.000783 lb/(ft/s) and m is in [lb] and g is 32 ft/s2 and t is time and v

Horizontal Range Calculation with air resistance

x=.1/.000783 *-5.28(1-e^(-.00783/.1).7)

x=3.677 ft which is approximately 1.2 meters

Without Air Resistance

x=(vicosQ)t

x=5.268(cos31.2)(.7)

x=3.16m

Assumptions made in theoretical calculations:

• neglect any air resistance,
• ignore ball spin
• there is no sideways error trajectory
• there is no error in the initial shooting velocity

these dimples "scope" the air in front and push it behind the ball. which prevents the pressure behind the ball from falling and the backwards motion that would cause. Also, air-flow above the ball travels faster which causes the air pressure on top of the ball to be less than the air pressure underneath it. This difference in pressure causes the ball to lift and stay in the air for a longer time.

The y position is affected by the applied

force and the gravitational force which

cause the parabola shape of the y position versus time graph

Y Velocity versus time graph

Initial Y Velocity as shown as a tangent line.

X Velocity Versus Time Graph

The initial velocity of y is 3.19m/s

• The graph displays the golf ball's change in velocity from up to down through the crossing of the origin